Problem: Recently Duff has been a soldier in the army. Malek is her commander.

Their country, Andarz Gu has n cities (numbered from 1 to n) and n - 1 bidirectional roads. Each road connects two different cities. There exist a unique path between any two cities.

There are also m people living in Andarz Gu (numbered from 1 to m). Each person has and ID number. ID number of i - th person is i and he/she lives in city number ci. Note that there may be more than one person in a city, also there may be no people living in the city.

<image>

Malek loves to order. That's why he asks Duff to answer to q queries. In each query, he gives her numbers v, u and a.

To answer a query:

Assume there are x people living in the cities lying on the path from city v to city u. Assume these people's IDs are p1, p2, ..., px in increasing order. 

If k = min(x, a), then Duff should tell Malek numbers k, p1, p2, ..., pk in this order. In the other words, Malek wants to know a minimums on that path (or less, if there are less than a people).

Duff is very busy at the moment, so she asked you to help her and answer the queries.

Input

The first line of input contains three integers, n, m and q (1 ≤ n, m, q ≤ 105).

The next n - 1 lines contain the roads. Each line contains two integers v and u, endpoints of a road (1 ≤ v, u ≤ n, v ≠ u).

Next line contains m integers c1, c2, ..., cm separated by spaces (1 ≤ ci ≤ n for each 1 ≤ i ≤ m).

Next q lines contain the queries. Each of them contains three integers, v, u and a (1 ≤ v, u ≤ n and 1 ≤ a ≤ 10).

Output

For each query, print numbers k, p1, p2, ..., pk separated by spaces in one line.

Examples

Input

5 4 5
1 3
1 2
1 4
4 5
2 1 4 3
4 5 6
1 5 2
5 5 10
2 3 3
5 3 1


Output

1 3
2 2 3
0
3 1 2 4
1 2

Note

Graph of Andarz Gu in the sample case is as follows (ID of people in each city are written next to them):

<image>

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int depth[100005], par[100003][21];
vector<int> ans[100001][19], g[100001];
inline void dfs(int pos, int prev) {
  depth[pos] = depth[prev] + 1;
  par[pos][0] = prev;
  for (int i = 0; i < g[pos].size(); i++) {
    if (g[pos][i] != prev) {
      dfs(g[pos][i], pos);
    }
  }
}
inline int lca(int x, int y) {
  if (depth[x] < depth[y]) {
    return lca(y, x);
  }
  int diff = depth[x] - depth[y];
  for (int i = 0; i <= 20; i++) {
    if (diff & (1 << i)) {
      x = par[x][i];
    }
  }
  if (x == y) {
    return x;
  }
  for (int i = 20; i >= 0; i--) {
    if (par[x][i] != par[y][i]) {
      x = par[x][i];
      y = par[y][i];
    }
  }
  return par[x][0];
}
inline vector<int> answer(int x, int y) {
  int z = lca(x, y);
  vector<int> ans1, ans2, fans;
  int diff = depth[x] - depth[z];
  for (int i = 0; i <= 18; i++) {
    if (diff & (1 << i)) {
      vector<int> temp;
      int u = 0, v = 0;
      while (temp.size() <= 9) {
        if (u < ans1.size()) {
          if (v < ans[x][i].size()) {
            if (ans1[u] <= ans[x][i][v]) {
              temp.push_back(ans1[u]);
              u++;
            } else {
              temp.push_back(ans[x][i][v]);
              v++;
            }
          } else {
            temp.push_back(ans1[u]);
            u++;
          }
        } else {
          if (v < ans[x][i].size()) {
            temp.push_back(ans[x][i][v]);
            v++;
          } else {
            break;
          }
        }
      }
      x = par[x][i];
      ans1 = temp;
    }
  }
  diff = depth[y] - depth[z];
  for (int i = 0; i <= 18; i++) {
    if (diff & (1 << i)) {
      vector<int> temp;
      int u = 0, v = 0;
      while (temp.size() <= 9) {
        if (u < ans2.size()) {
          if (v < ans[y][i].size()) {
            if (ans2[u] <= ans[y][i][v]) {
              temp.push_back(ans2[u]);
              u++;
            } else {
              temp.push_back(ans[y][i][v]);
              v++;
            }
          } else {
            temp.push_back(ans2[u]);
            u++;
          }
        } else {
          if (v < ans[y][i].size()) {
            temp.push_back(ans[y][i][v]);
            v++;
          } else {
            break;
          }
        }
      }
      y = par[y][i];
      ans2 = temp;
    }
  }
  vector<int> temp;
  int u = 0, v = 0;
  while (temp.size() <= 9) {
    if (u < ans1.size()) {
      if (v < ans[z][0].size()) {
        if (ans1[u] <= ans[z][0][v]) {
          temp.push_back(ans1[u]);
          u++;
        } else {
          temp.push_back(ans[z][0][v]);
          v++;
        }
      } else {
        temp.push_back(ans1[u]);
        u++;
      }
    } else {
      if (v < ans[z][0].size()) {
        temp.push_back(ans[z][0][v]);
        v++;
      } else {
        break;
      }
    }
  }
  ans1 = temp;
  int i = 0, j = 0;
  while (fans.size() <= 9) {
    if (i < ans1.size()) {
      if (j < ans2.size()) {
        if (ans1[i] <= ans2[j]) {
          fans.push_back(ans1[i]);
          i++;
        } else {
          fans.push_back(ans2[j]);
          j++;
        }
      } else {
        fans.push_back(ans1[i]);
        i++;
      }
    } else {
      if (j < ans2.size()) {
        fans.push_back(ans2[j]);
        j++;
      } else {
        break;
      }
    }
  }
  return fans;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  int n, m, q;
  cin >> n >> m >> q;
  int x, y, a;
  for (int i = 1; i < n; i++) {
    cin >> x >> y;
    g[x].push_back(y);
    g[y].push_back(x);
  }
  dfs(1, 0);
  for (int i = 1; i <= 20; i++) {
    for (int j = 1; j <= n; j++) {
      par[j][i] = par[par[j][i - 1]][i - 1];
    }
  }
  for (int i = 1; i <= m; i++) {
    cin >> x;
    if (ans[x][0].size() <= 9) ans[x][0].push_back(i);
  }
  for (int i = 1; i <= 18; i++) {
    for (int j = 1; j <= n; j++) {
      int u = 0, v = 0;
      while (ans[j][i].size() <= 9) {
        if (u < ans[j][i - 1].size()) {
          if (v < ans[par[j][i - 1]][i - 1].size()) {
            if (ans[j][i - 1][u] <= ans[par[j][i - 1]][i - 1][v]) {
              ans[j][i].push_back(ans[j][i - 1][u]);
              u++;
            } else {
              ans[j][i].push_back(ans[par[j][i - 1]][i - 1][v]);
              v++;
            }
          } else {
            ans[j][i].push_back(ans[j][i - 1][u]);
            u++;
          }
        } else {
          if (v < ans[par[j][i - 1]][i - 1].size()) {
            ans[j][i].push_back(ans[par[j][i - 1]][i - 1][v]);
            v++;
          } else {
            break;
          }
        }
      }
    }
  }
  while (q--) {
    cin >> x >> y >> a;
    vector<int> res = answer(x, y);
    cout << min((int)res.size(), a) << " ";
    for (int i = 0; i < min(a, (int)res.size()); i++) {
      cout << res[i] << " ";
    }
    cout << "\n";
  }
}